The teacher asks Bill to calculate $a-b-c$, but Bill mistakenly calculates $a-(b-c)$ and gets an answer of 11. If the correct answer was 3, what is the value of $a-b$?
Instead of calculating $a - b - c$, Bill calculated $a - b + c$.  Therefore, the value of $a - b$ is simply the average of the two, making for $\frac{11+3}{2} = \boxed{7}$.